Abstarct: In recent years production of complex industrial products with purpose of increasing in strength-to-weight ratio and reducing vehicle fuel consumption have been focused by researchers. In this regard, the new methods of mextal forming such as high energy rate forming that included explosive forming, electrohydraulic forming and electromagnetic forming have been used. The most important feature of these processes is releasing high energy in a very short time and production very high contact pressure. The numerous experimental and theoretical researches in recent years showed that in high energy rate forming processes, under the effect of through thickness stress, the formability had been greatly increased. In this study in order to achieve an exact analytical solution for investigate the effect of stress in thickness direction on plastic instability created in sheet mextal, Swift diffuse neck theory is used. The assumption used for sheet material included rigid-plastic behavior, power low hardening equation and normal plastic anisotropy with regardless of the plane anisotropy of sheet. Driving the plastic flow rule for quadratic and non-quadratic Hill's yield criterion in the general case (with the presence of normal stress component) first the constants of yield criterion was calculated baxsed on the anisotropy coefficients of sheet and then critical stress and strain were extracted on the eve of diffuse neck. To investigate the effect of through thickness stress on forming limit diagram of AA6011 sheet, using the experimental data of the reference article, the acceptable exponent of yield criterion and forming limit diagrams at different pressure ratios were obtained. The results of this part showed that the formability increases with increase of normal pressure . On the numerical solution, in tube bulging process using elastic pad, the prediction of tearing in steel tube, by using forming limit diagram has been carried out.